Star-type oscillatory networks with generic Kuramoto-type coupling: a model for "Japanese drums synchrony"

TL;DR

This paper models a drum orchestra using star-type networks of phase oscillators with Kuramoto-type coupling, analyzing synchronization states analytically for identical oscillators and numerically for nonidentical ones.

Contribution

It introduces a novel star-type oscillator network model for drum synchrony, combining analytical and numerical methods to study stability and dynamics.

Findings

Analytical solutions for identical oscillators' states.

Numerical stability analysis for nonidentical oscillators.

Model effectively captures drum orchestra synchronization.

Abstract

We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra.